Finite rank elements in semisimple Banach algebras

• Autorzy: Matej Brešar , Peter Šemrl
• Języki publikacji: EN

Abstrakty

EN

Let A be a semisimple Banach algebra. We define the rank of a nonzero element a in the socle of A to be the minimum of the number of minimal left ideals whose sum contains a. Several characterizations of rank are proved.

Kategorie tematyczne

• 46H15: Representations of topological algebras
• 46H05: General theory of topological algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 128
• Numer: 3
• Strony: 287-298

Daty

wydano

1998

otrzymano

1997-07-15

poprawiono

1997-10-29

Twórcy

autor

Matej Brešar

• University of Maribor, PF, Koroška 160, 2000 Maribor, Slovenia

autor

Peter Šemrl

• University of Maribor, SF, Smetanova 17, 2000 Maribor, Slovenia

Bibliografia

• [1] J. C. Alexander, Compact Banach algebras, Proc. London Math. Soc. 18 (1968), 1-18.
• [2] B. Aupetit and T. Mouton, Spectrum-preserving linear mappings in Banach algebras, Studia Math. 109 (1994), 91-100.
• [3] B. Aupetit and T. Mouton, Trace and determinant in Banach algebras, ibid. 121 (1996), 115-136.
• [4] M. Brešar and P. Šemrl, Derivations mapping into the socle, Math. Proc. Cambridge Philos. Soc. 120 (1996), 339-346.
• [5] J. M. G. Fell and R. S. Doran, Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles, Vol. 1, Academic Press, Boston, 1988.
• [6] A. A. Jafarian and A. R. Sourour, Spectrum preserving linear maps, J. Funct. Anal. 66 (1986), 255-261.
• [7] B. V. Limaye, A spectral characterization of operators having rank k, Linear Algebra Appl. 143 (1991), 57-66.
• [8] T. Mouton and H. Raubenheimer, On rank one and finite elements of Banach algebras, Studia Math. 104 (1993), 211-219.
• [9] P. Nylen and L. Rodman, Approximation numbers and Yamamoto's theorem in Banach algebras, Integral Equations Operator Theory 13 (1990), 728-749.
• [10] C. E. Rickart, General Theory of Banach Algebras, The University Series in Higher Mathematics, D. van Nostrand, 1960.